Block #1,073,563

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/24/2015, 11:36:40 AM · Difficulty 10.7404 · 5,768,321 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e05c2adaeb43cfe6e0a5321b5da91a9506b933b79009830a971f81dbc22d70ba

View on Chainz ↗

Height

#1,073,563

Difficulty

10.740369

Transactions

Size

10.11 KB

Version

Bits

0abd88d0

Nonce

1,958,128,495

Timestamp

5/24/2015, 11:36:40 AM

Confirmations

5,768,321

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

000d43190c08fbdd5b978bd3954a370fa27d6d003ae7b013cd9fd827ca6dc735

Transactions (2)

Coinbase2bf29dd3904afb…5291b2d047c15c

1 in → 1 out9.2900 XPM116 B

ANSXnLY2…Sd25TjkD

5a92ffbd3446bd…8a47d86e56244e

68 in → 2 out3797.8099 XPM9.91 KB

AamvfYr2…qExEMdKh AME5qxae…KBcf1ejr

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.

2.661 × 10⁹⁸(99-digit number)

26612740694764274043…01591023247836876799

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

2.661 × 10⁹⁸(99-digit number)

26612740694764274043…01591023247836876799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.661 × 10⁹⁸(99-digit number)

26612740694764274043…01591023247836876801

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

5.322 × 10⁹⁸(99-digit number)

53225481389528548086…03182046495673753599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.322 × 10⁹⁸(99-digit number)

53225481389528548086…03182046495673753601

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

1.064 × 10⁹⁹(100-digit number)

10645096277905709617…06364092991347507199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.064 × 10⁹⁹(100-digit number)

10645096277905709617…06364092991347507201

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

2.129 × 10⁹⁹(100-digit number)

21290192555811419234…12728185982695014399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.129 × 10⁹⁹(100-digit number)

21290192555811419234…12728185982695014401

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

4.258 × 10⁹⁹(100-digit number)

42580385111622838469…25456371965390028799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.258 × 10⁹⁹(100-digit number)

42580385111622838469…25456371965390028801

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 #1,073,563

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