Block #960,439

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/3/2015, 11:39:33 PM · Difficulty 10.8858 · 5,838,481 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dfba2cefc4a891dd1b4a8fb33aed6887f1112de275b886455601caed03f5b851

View on Chainz ↗

Height

#960,439

Difficulty

10.885790

Transactions

Size

651 B

Version

Bits

0ae2c31e

Nonce

1,742,818,917

Timestamp

3/3/2015, 11:39:33 PM

Confirmations

5,838,481

Mined by

⛏️ P2SHAP6Fq7G7yYD35eaA9Qttx2S88vK9o6stFS

Merkle Root

5c5f03eba1fb40d0a99fd44b8110b257a363812d78c527cc148a02eafa82a2ef

Transactions (3)

Coinbase6630776cc99f9d…60f148886afdf0

1 in → 1 out8.4500 XPM109 B

AP6Fq7G7…K9o6stFS

3caa7ea6b04049…4a8fe47ef10d75

1 in → 2 out8.3900 XPM225 B

Ae7YXEyn…hnSYZsCr AbQtdbiK…UnVhiV8w

37346861ee251c…d2dc26d6f6a7f7

1 in → 2 out7.7202 XPM226 B

Adu2uGcK…YG6X3cBK ANfmUrFA…kVSzdPqM

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.

3.232 × 10⁹⁶(97-digit number)

32327538167613224534…25688209812948418559

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

3.232 × 10⁹⁶(97-digit number)

32327538167613224534…25688209812948418559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.232 × 10⁹⁶(97-digit number)

32327538167613224534…25688209812948418561

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

6.465 × 10⁹⁶(97-digit number)

64655076335226449069…51376419625896837119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.465 × 10⁹⁶(97-digit number)

64655076335226449069…51376419625896837121

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

1.293 × 10⁹⁷(98-digit number)

12931015267045289813…02752839251793674239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.293 × 10⁹⁷(98-digit number)

12931015267045289813…02752839251793674241

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

2.586 × 10⁹⁷(98-digit number)

25862030534090579627…05505678503587348479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.586 × 10⁹⁷(98-digit number)

25862030534090579627…05505678503587348481

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

5.172 × 10⁹⁷(98-digit number)

51724061068181159255…11011357007174696959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.172 × 10⁹⁷(98-digit number)

51724061068181159255…11011357007174696961

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