Block #855,275

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/16/2014, 5:50:52 AM · Difficulty 10.9684 · 5,985,952 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cb1b071c98a583a40d6b8889208c534413eb91d6a02c192394b34ce18d0a03e6

View on Chainz ↗

Height

#855,275

Difficulty

10.968378

Transactions

Size

659 B

Version

Bits

0af7e79e

Nonce

122,303,814

Timestamp

12/16/2014, 5:50:52 AM

Confirmations

5,985,952

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e9ce6ea3de550883e51f2af18ffd56bf25e35fc2bb45bab33c2a4430c9774361

Transactions (3)

Coinbaseb545e711c3b1ea…cedcfd36c838ab

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

cec146bb4b306c…4ab202a2ebe0b4

1 in → 2 out0.0897 XPM227 B

APU23ocp…vTcGKv94 AerJD7z6…dJqpAxSw

76cbd6316ecc83…f176783af3d596

1 in → 2 out0.0906 XPM225 B

AY3vCB2Z…3UTRbsmW AHFSdA6b…JpzSeQ4x

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.

3.955 × 10⁹⁶(97-digit number)

39557689086475312843…14879768022223316239

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

3.955 × 10⁹⁶(97-digit number)

39557689086475312843…14879768022223316239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.955 × 10⁹⁶(97-digit number)

39557689086475312843…14879768022223316241

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

7.911 × 10⁹⁶(97-digit number)

79115378172950625686…29759536044446632479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.911 × 10⁹⁶(97-digit number)

79115378172950625686…29759536044446632481

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

1.582 × 10⁹⁷(98-digit number)

15823075634590125137…59519072088893264959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.582 × 10⁹⁷(98-digit number)

15823075634590125137…59519072088893264961

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

3.164 × 10⁹⁷(98-digit number)

31646151269180250274…19038144177786529919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.164 × 10⁹⁷(98-digit number)

31646151269180250274…19038144177786529921

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

6.329 × 10⁹⁷(98-digit number)

63292302538360500549…38076288355573059839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.329 × 10⁹⁷(98-digit number)

63292302538360500549…38076288355573059841

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 #855,275

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