Block #1,102,853

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/13/2015, 4:13:21 PM · Difficulty 10.7521 · 5,736,538 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

00bd51f3d862c2bfa2f15bc277128f8e0e84096e91b16e905014c13755a735f6

View on Chainz ↗

Height

#1,102,853

Difficulty

10.752118

Transactions

Size

2.87 KB

Version

Bits

0ac08ac7

Nonce

808,243,704

Timestamp

6/13/2015, 4:13:21 PM

Confirmations

5,736,538

Mined by

⛏️ P2SHAWncmyiPe26k8yR7P6ujJTGjj5so9CCvGQ

Merkle Root

860ef11282b6c3f898c6d3d51ffb77e7f84478f2800cf78f31795e9f57f4ce63

Transactions (2)

Coinbasefeed08d2870162…546e3e07f839e4

1 in → 1 out8.7100 XPM109 B

AWncmyiP…so9CCvGQ

e623b96c6a4078…a3239cb5d5105d

18 in → 2 out400.0100 XPM2.68 KB

AMX5PJZH…Qa4HHBji AYHqVxeQ…xdtpawf5

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.

4.451 × 10⁹²(93-digit number)

44510893610572799563…90882948134410589439

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

4.451 × 10⁹²(93-digit number)

44510893610572799563…90882948134410589439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.451 × 10⁹²(93-digit number)

44510893610572799563…90882948134410589441

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

8.902 × 10⁹²(93-digit number)

89021787221145599126…81765896268821178879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.902 × 10⁹²(93-digit number)

89021787221145599126…81765896268821178881

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

1.780 × 10⁹³(94-digit number)

17804357444229119825…63531792537642357759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.780 × 10⁹³(94-digit number)

17804357444229119825…63531792537642357761

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

3.560 × 10⁹³(94-digit number)

35608714888458239650…27063585075284715519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.560 × 10⁹³(94-digit number)

35608714888458239650…27063585075284715521

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

7.121 × 10⁹³(94-digit number)

71217429776916479300…54127170150569431039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.121 × 10⁹³(94-digit number)

71217429776916479300…54127170150569431041

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 #1,102,853

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