Block #611,460

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/2/2014, 4:33:34 AM · Difficulty 10.9225 · 6,191,898 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

680a664a098a0e2e4603588a1f45e174ead904834b3fad99ddbf94eb3d4c9c1c

View on Chainz ↗

Height

#611,460

Difficulty

10.922459

Transactions

Size

1.73 KB

Version

Bits

0aec264c

Nonce

895,305,780

Timestamp

7/2/2014, 4:33:34 AM

Confirmations

6,191,898

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

04307a7ed3d0764b76fd6893a34f7775a7143a93b642eca65ad6a177a5dda08d

Transactions (4)

Coinbasede4765f02f0027…23662d6962ae4c

1 in → 1 out8.4100 XPM116 B

ANSXnLY2…Sd25TjkD

144aa83e67cce3…beb411aba77f86

6 in → 2 out69.8266 XPM966 B

AR3NsN6L…zoMC9e95 AbAcrWWU…QuqrJku9

12b0af5f841888…f5d8cd8dbbfe10

2 in → 2 out7.7317 XPM374 B

AHWKKQVm…QPbiQck8 AXoVHUMB…6LtFTHnw

1d99beb2f06cf6…58381cff4b51d0

1 in → 2 out4.7466 XPM225 B

APCeUUmp…p9ZodcX1 AWr7QESV…T91HodnJ

Prime Chain Origin

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

1.956 × 10⁹⁶(97-digit number)

19565285675906920485…41231316248890678399

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

1.956 × 10⁹⁶(97-digit number)

19565285675906920485…41231316248890678399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.956 × 10⁹⁶(97-digit number)

19565285675906920485…41231316248890678401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

3.913 × 10⁹⁶(97-digit number)

39130571351813840970…82462632497781356799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.913 × 10⁹⁶(97-digit number)

39130571351813840970…82462632497781356801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

7.826 × 10⁹⁶(97-digit number)

78261142703627681941…64925264995562713599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.826 × 10⁹⁶(97-digit number)

78261142703627681941…64925264995562713601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.565 × 10⁹⁷(98-digit number)

15652228540725536388…29850529991125427199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.565 × 10⁹⁷(98-digit number)

15652228540725536388…29850529991125427201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

3.130 × 10⁹⁷(98-digit number)

31304457081451072776…59701059982250854399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.130 × 10⁹⁷(98-digit number)

31304457081451072776…59701059982250854401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer