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Block #12,089

TWNLength 7β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/11/2013, 8:45:03 AM Β· Difficulty 7.7468 Β· 6,815,282 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6761383bc4188b0320126fb50be776921da1bc123334db6d3cee7a1185679c7c
View on Chainz β†—

Height

#12,089

Difficulty

7.746761

Transactions

1

Size

198 B

Version

2

Bits

07bf2bbd

Nonce

238

Timestamp

7/11/2013, 8:45:03 AM

Confirmations

6,815,282

Mined by

⛏️ 7AMD88WR9uHG5EGxCCpAkcCRBhfZhWoLU4a

Merkle Root

98f59b6f09f0d2d45ac98f4275db98d8022da01223114c2c55b6c8f1df76e274
Transactions (1)
Coinbase98f59b6f09f0d2…b6c8f1df76e274
1 in β†’ 1 out16.6400 XPM108 B
AMD88WR9…ZhWoLU4a
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

8.523 Γ— 10⁹⁴(95-digit number)
85234951706743668147…40240486592522472739
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
8.523 Γ— 10⁹⁴(95-digit number)
85234951706743668147…40240486592522472739
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.523 Γ— 10⁹⁴(95-digit number)
85234951706743668147…40240486592522472741
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.704 Γ— 10⁹⁡(96-digit number)
17046990341348733629…80480973185044945479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.704 Γ— 10⁹⁡(96-digit number)
17046990341348733629…80480973185044945481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
3.409 Γ— 10⁹⁡(96-digit number)
34093980682697467259…60961946370089890959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.409 Γ— 10⁹⁡(96-digit number)
34093980682697467259…60961946370089890961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
6.818 Γ— 10⁹⁡(96-digit number)
68187961365394934518…21923892740179781919
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 7

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,863,069 XPMΒ·at block #6,827,370 Β· updates every 60s
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