Block #1,111,785

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/17/2015, 1:57:02 AM · Difficulty 10.8887 · 5,715,136 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

631d427727960a81d667c72d1233889fc62a237a0fce2fdbfe42b5d35ef4e5ff

View on Chainz ↗

Height

#1,111,785

Difficulty

10.888683

Transactions

Size

6.35 KB

Version

Bits

0ae380b7

Nonce

320,261,622

Timestamp

6/17/2015, 1:57:02 AM

Confirmations

5,715,136

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

37e66e31cb602fa6185376c3f23563f60b082b586fb07572ed7c14bd357a795e

Transactions (2)

Coinbase4a0b5c99da73aa…54b60ee624c160

1 in → 1 out8.4900 XPM116 B

AJCEY9yy…tg97E6zm

721ccaee2912cc…e96a80c7977f38

42 in → 2 out121.0274 XPM6.15 KB

Aar9FsrJ…edtvXPS7 AaxCzsay…bAqhqJEy

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.

3.599 × 10⁹⁶(97-digit number)

35995083483277863799…62424961059611176959

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

3.599 × 10⁹⁶(97-digit number)

35995083483277863799…62424961059611176959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.599 × 10⁹⁶(97-digit number)

35995083483277863799…62424961059611176961

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

7.199 × 10⁹⁶(97-digit number)

71990166966555727599…24849922119222353919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.199 × 10⁹⁶(97-digit number)

71990166966555727599…24849922119222353921

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

1.439 × 10⁹⁷(98-digit number)

14398033393311145519…49699844238444707839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.439 × 10⁹⁷(98-digit number)

14398033393311145519…49699844238444707841

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

2.879 × 10⁹⁷(98-digit number)

28796066786622291039…99399688476889415679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.879 × 10⁹⁷(98-digit number)

28796066786622291039…99399688476889415681

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

5.759 × 10⁹⁷(98-digit number)

57592133573244582079…98799376953778831359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.759 × 10⁹⁷(98-digit number)

57592133573244582079…98799376953778831361

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 #1,111,785

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