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Block #2,039,177

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/26/2017, 9:09:21 AM Β· Difficulty 10.6805 Β· 4,801,540 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9ace443e138a370db0dd8843c6226c1e49dad33c02bbb68c559983474f436074
View on Chainz β†—

Height

#2,039,177

Difficulty

10.680493

Transactions

1

Size

210 B

Version

2

Bits

0aae34cb

Nonce

208,033,089

Timestamp

3/26/2017, 9:09:21 AM

Confirmations

4,801,540

Mined by

⛏️ P2SHAM6GYpjwZFjhLNzHZAfmRp8jwiaw86QDtR

Merkle Root

2d15ea2dd66e50bc1626029caebcd39eae1f5d914a34e7714590f955295f12c7
Transactions (1)
Coinbase2d15ea2dd66e50…90f955295f12c7
1 in β†’ 1 out8.7500 XPM118 B
AM6GYpjw…aw86QDtR
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.

1.044 Γ— 10⁹⁹(100-digit number)
10447593201875592951…82386853903345950719
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
1.044 Γ— 10⁹⁹(100-digit number)
10447593201875592951…82386853903345950719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.044 Γ— 10⁹⁹(100-digit number)
10447593201875592951…82386853903345950721
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
2.089 Γ— 10⁹⁹(100-digit number)
20895186403751185903…64773707806691901439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.089 Γ— 10⁹⁹(100-digit number)
20895186403751185903…64773707806691901441
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
4.179 Γ— 10⁹⁹(100-digit number)
41790372807502371807…29547415613383802879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.179 Γ— 10⁹⁹(100-digit number)
41790372807502371807…29547415613383802881
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
8.358 Γ— 10⁹⁹(100-digit number)
83580745615004743614…59094831226767605759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.358 Γ— 10⁹⁹(100-digit number)
83580745615004743614…59094831226767605761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.671 Γ— 10¹⁰⁰(101-digit number)
16716149123000948722…18189662453535211519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.671 Γ— 10¹⁰⁰(101-digit number)
16716149123000948722…18189662453535211521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 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
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 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
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