Block #1,271,083

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/7/2015, 2:55:51 PM · Difficulty 10.8166 · 5,554,454 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

22e42cc0f6de00c9e5dc3dca8aee6a32dd22508ac74b8341c4eb0662deb5ff53

View on Chainz ↗

Height

#1,271,083

Difficulty

10.816627

Transactions

Size

658 B

Version

Bits

0ad10e70

Nonce

17,463,819

Timestamp

10/7/2015, 2:55:51 PM

Confirmations

5,554,454

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

f8f2ea252bb1bbfb53a35c45af5a6d52d57986f0254784f66a08d97ea1b51902

Transactions (3)

Coinbase5bc3c303357748…af9c6334dbcebe

1 in → 1 out8.5500 XPM116 B

AJCEY9yy…tg97E6zm

b51c7d44613164…1e597d2e38553f

1 in → 2 out6.0128 XPM226 B

AeBwvm57…kL6E7ayF AVZ9PqaY…bn5a5eSS

95fbf463dc706a…200bcbb05bb44a

1 in → 2 out1.1119 XPM225 B

AbY6jpKm…xfyDrP1G AU1tZNJn…osuhqZ1i

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.

4.783 × 10⁹⁶(97-digit number)

47834678994732250130…45192420649191047999

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

4.783 × 10⁹⁶(97-digit number)

47834678994732250130…45192420649191047999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.783 × 10⁹⁶(97-digit number)

47834678994732250130…45192420649191048001

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

9.566 × 10⁹⁶(97-digit number)

95669357989464500261…90384841298382095999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.566 × 10⁹⁶(97-digit number)

95669357989464500261…90384841298382096001

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

1.913 × 10⁹⁷(98-digit number)

19133871597892900052…80769682596764191999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.913 × 10⁹⁷(98-digit number)

19133871597892900052…80769682596764192001

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

3.826 × 10⁹⁷(98-digit number)

38267743195785800104…61539365193528383999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.826 × 10⁹⁷(98-digit number)

38267743195785800104…61539365193528384001

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

7.653 × 10⁹⁷(98-digit number)

76535486391571600209…23078730387056767999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.653 × 10⁹⁷(98-digit number)

76535486391571600209…23078730387056768001

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 #1,271,083

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