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Block #717,912

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/12/2014, 8:38:22 PM Β· Difficulty 10.9500 Β· 6,087,941 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8ee60712c6977f5be9c29a20165910a12d2e1c286205515a2319a09124c6c07a
View on Chainz β†—

Height

#717,912

Difficulty

10.949979

Transactions

2

Size

875 B

Version

2

Bits

0af331d4

Nonce

1,336,353,492

Timestamp

9/12/2014, 8:38:22 PM

Confirmations

6,087,941

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

dcd4fbc6db443376c132967424c4fac93b7f96c770d13bb8a54fa9bc48f99498
Transactions (2)
Coinbasec586efb31b916f…4afc7427cfe205
1 in β†’ 1 out8.3400 XPM116 B
ANSXnLY2…Sd25TjkD
cb85efc88d2fa8…c6bef416c26959
4 in β†’ 2 out3369.9100 XPM669 B
AHVR9HWr…jByRHGQAAMKNcVrn…X8cHm7Um
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.

3.301 Γ— 10⁹⁴(95-digit number)
33012729456599547771…65885508512409236319
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
3.301 Γ— 10⁹⁴(95-digit number)
33012729456599547771…65885508512409236319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.301 Γ— 10⁹⁴(95-digit number)
33012729456599547771…65885508512409236321
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
6.602 Γ— 10⁹⁴(95-digit number)
66025458913199095543…31771017024818472639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.602 Γ— 10⁹⁴(95-digit number)
66025458913199095543…31771017024818472641
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
1.320 Γ— 10⁹⁡(96-digit number)
13205091782639819108…63542034049636945279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.320 Γ— 10⁹⁡(96-digit number)
13205091782639819108…63542034049636945281
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
2.641 Γ— 10⁹⁡(96-digit number)
26410183565279638217…27084068099273890559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.641 Γ— 10⁹⁡(96-digit number)
26410183565279638217…27084068099273890561
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
5.282 Γ— 10⁹⁡(96-digit number)
52820367130559276434…54168136198547781119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.282 Γ— 10⁹⁡(96-digit number)
52820367130559276434…54168136198547781121
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
1.056 Γ— 10⁹⁢(97-digit number)
10564073426111855286…08336272397095562239
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:57,690,905 XPMΒ·at block #6,805,852 Β· updates every 60s
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