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Block #1,231,522

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/11/2015, 8:49:16 AM Β· Difficulty 10.7387 Β· 5,593,383 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1548555dfd2042e10a04ebe260eae4fe31d49975fcb0f2e06c50c45d6df6a35f
View on Chainz β†—

Height

#1,231,522

Difficulty

10.738697

Transactions

2

Size

3.88 KB

Version

2

Bits

0abd1b3b

Nonce

282,474,756

Timestamp

9/11/2015, 8:49:16 AM

Confirmations

5,593,383

Mined by

⛏️ P2SHAMsJB7AuWuQRmqhwNaFiJ46bSxRz6PZuJe

Merkle Root

aabd5855efd70ffa251e666a83d82ac40a02f8494067d4972017f95efab83143
Transactions (2)
Coinbase7fed590f74167a…46c4973c2eb824
1 in β†’ 1 out8.7000 XPM109 B
AMsJB7Au…Rz6PZuJe
f90eab59a832a3…34b1d337c6b949
25 in β†’ 2 out135.7714 XPM3.69 KB
AQHE5e6H…xDwU3vYUAaYBjG29…N9UDhHmA
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.

1.061 Γ— 10⁹³(94-digit number)
10618575866942468866…44522753637818509389
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
1.061 Γ— 10⁹³(94-digit number)
10618575866942468866…44522753637818509389
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.061 Γ— 10⁹³(94-digit number)
10618575866942468866…44522753637818509391
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
2.123 Γ— 10⁹³(94-digit number)
21237151733884937732…89045507275637018779
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.123 Γ— 10⁹³(94-digit number)
21237151733884937732…89045507275637018781
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
4.247 Γ— 10⁹³(94-digit number)
42474303467769875464…78091014551274037559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.247 Γ— 10⁹³(94-digit number)
42474303467769875464…78091014551274037561
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
8.494 Γ— 10⁹³(94-digit number)
84948606935539750928…56182029102548075119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.494 Γ— 10⁹³(94-digit number)
84948606935539750928…56182029102548075121
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
1.698 Γ— 10⁹⁴(95-digit number)
16989721387107950185…12364058205096150239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.698 Γ— 10⁹⁴(95-digit number)
16989721387107950185…12364058205096150241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,843,323 XPMΒ·at block #6,824,904 Β· updates every 60s
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