XPM Prime Explorer symbol
XPMPrime Explorer

Block #641,020

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/20/2014, 4:23:10 PM Β· Difficulty 10.9576 Β· 6,165,162 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
f9daa2a0ed99d1558cbe7b00d0352d584909dcccef650222d153e5593da94b57
View on Chainz β†—

Height

#641,020

Difficulty

10.957559

Transactions

2

Size

878 B

Version

2

Bits

0af52292

Nonce

697,922,983

Timestamp

7/20/2014, 4:23:10 PM

Confirmations

6,165,162

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

6a75624dcf2dba68eb4d92c4c16fb1a2733edb3ad4a49de8b1c40ef42b4d2373
Transactions (2)
Coinbase0f94c128a09901…3d59a30eb0126b
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
b7c468758cfce5…920c4570e39765
4 in β†’ 2 out6.8606 XPM670 B
AesRMui3…NhroyfkvAbDfqXPx…WFB2hCFv
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.995 Γ— 10⁹⁸(99-digit number)
39953178343675382487…10130242630105681919
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
3.995 Γ— 10⁹⁸(99-digit number)
39953178343675382487…10130242630105681919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.995 Γ— 10⁹⁸(99-digit number)
39953178343675382487…10130242630105681921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
7.990 Γ— 10⁹⁸(99-digit number)
79906356687350764974…20260485260211363839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.990 Γ— 10⁹⁸(99-digit number)
79906356687350764974…20260485260211363841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.598 Γ— 10⁹⁹(100-digit number)
15981271337470152994…40520970520422727679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.598 Γ— 10⁹⁹(100-digit number)
15981271337470152994…40520970520422727681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
3.196 Γ— 10⁹⁹(100-digit number)
31962542674940305989…81041941040845455359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.196 Γ— 10⁹⁹(100-digit number)
31962542674940305989…81041941040845455361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
6.392 Γ— 10⁹⁹(100-digit number)
63925085349880611979…62083882081690910719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.392 Γ— 10⁹⁹(100-digit number)
63925085349880611979…62083882081690910721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.278 Γ— 10¹⁰⁰(101-digit number)
12785017069976122395…24167764163381821439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,693,540 XPMΒ·at block #6,806,181 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK