XPM Prime Explorer symbol
XPMPrime Explorer

Block #680,208

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/16/2014, 1:49:22 PM Β· Difficulty 10.9624 Β· 6,119,138 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5c5c913b3e10c349935f23ed5ce5f6c504958b11d7814834b9669dba0e56b557
View on Chainz β†—

Height

#680,208

Difficulty

10.962433

Transactions

2

Size

433 B

Version

2

Bits

0af66207

Nonce

209,633,129

Timestamp

8/16/2014, 1:49:22 PM

Confirmations

6,119,138

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

87b43069239e3c4f939dbbc2ab7111c395b05e9b4ca739805bbdba05966451cc
Transactions (2)
Coinbase30170bac60d598…8192d892719f8d
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
9a95f85df7b2ff…4174754ee24e69
1 in β†’ 2 out8.2900 XPM227 B
AaQjQY9o…X8tz6TgJAXtGFfPj…UY8uHkHy
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.

5.689 Γ— 10⁹⁴(95-digit number)
56892157798296079876…48373701245296081119
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
5.689 Γ— 10⁹⁴(95-digit number)
56892157798296079876…48373701245296081119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.689 Γ— 10⁹⁴(95-digit number)
56892157798296079876…48373701245296081121
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
1.137 Γ— 10⁹⁡(96-digit number)
11378431559659215975…96747402490592162239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.137 Γ— 10⁹⁡(96-digit number)
11378431559659215975…96747402490592162241
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
2.275 Γ— 10⁹⁡(96-digit number)
22756863119318431950…93494804981184324479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.275 Γ— 10⁹⁡(96-digit number)
22756863119318431950…93494804981184324481
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
4.551 Γ— 10⁹⁡(96-digit number)
45513726238636863901…86989609962368648959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.551 Γ— 10⁹⁡(96-digit number)
45513726238636863901…86989609962368648961
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
9.102 Γ— 10⁹⁡(96-digit number)
91027452477273727802…73979219924737297919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.102 Γ— 10⁹⁡(96-digit number)
91027452477273727802…73979219924737297921
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
1.820 Γ— 10⁹⁢(97-digit number)
18205490495454745560…47958439849474595839
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:57,638,820 XPMΒ·at block #6,799,345 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