Block #616,034

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/4/2014, 8:03:24 AM · Difficulty 10.9424 · 6,198,436 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e388ff7429fb636288098e7d88432ebb7dc7175aacc696416ddbeca719217500

View on Chainz ↗

Height

#616,034

Difficulty

10.942369

Transactions

Size

657 B

Version

Bits

0af13f1b

Nonce

1,508,331,939

Timestamp

7/4/2014, 8:03:24 AM

Confirmations

6,198,436

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

6e77c641f506dbae8c5eb6c1f2dbd4459f1e2a4a6ac31307cb65fd17c462debe

Transactions (3)

Coinbase6eb47c8d6166ab…7f1a42f0a76e6a

1 in → 1 out8.3600 XPM116 B

ANSXnLY2…Sd25TjkD

921f9fbad73da6…c8adc660e8da16

1 in → 2 out3.1021 XPM225 B

AS9ZCvju…bu3NEFwZ ANV5xG2t…5vVyDrDJ

bcfedf20bac8fc…0c52e8a5060c70

1 in → 2 out1.5471 XPM225 B

Ae2e83MX…bzxmuQ39 Abcb7dVg…i9mx5XXc

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.

9.311 × 10⁹⁵(96-digit number)

93118759261024101301…94399618264594474399

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

9.311 × 10⁹⁵(96-digit number)

93118759261024101301…94399618264594474399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.311 × 10⁹⁵(96-digit number)

93118759261024101301…94399618264594474401

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

1.862 × 10⁹⁶(97-digit number)

18623751852204820260…88799236529188948799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.862 × 10⁹⁶(97-digit number)

18623751852204820260…88799236529188948801

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

3.724 × 10⁹⁶(97-digit number)

37247503704409640520…77598473058377897599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.724 × 10⁹⁶(97-digit number)

37247503704409640520…77598473058377897601

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

7.449 × 10⁹⁶(97-digit number)

74495007408819281040…55196946116755795199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.449 × 10⁹⁶(97-digit number)

74495007408819281040…55196946116755795201

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

1.489 × 10⁹⁷(98-digit number)

14899001481763856208…10393892233511590399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.489 × 10⁹⁷(98-digit number)

14899001481763856208…10393892233511590401

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

Block #616,034

Cookie Preferences