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Block #1,684,940

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/22/2016, 4:46:36 PM Β· Difficulty 10.7229 Β· 5,156,965 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3c883f5c5f7c3c8a1f41a4de0c88f28424b177fbc9e266db799a380095d1d294
View on Chainz β†—

Height

#1,684,940

Difficulty

10.722879

Transactions

1

Size

200 B

Version

2

Bits

0ab90e9b

Nonce

445,444,126

Timestamp

7/22/2016, 4:46:36 PM

Confirmations

5,156,965

Mined by

⛏️ P2SHAayDkAhKDJ4XJxp3FBmoGvUyMFRbtvAqQQ

Merkle Root

f671c5b81c31c8af097370171ad3f51d5be60771cbb84d9eb5cc2fe39dd6947d
Transactions (1)
Coinbasef671c5b81c31c8…cc2fe39dd6947d
1 in β†’ 1 out8.6800 XPM109 B
AayDkAhK…RbtvAqQQ
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.

1.262 Γ— 10⁹⁷(98-digit number)
12626544056231415903…54023146934338355199
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
1.262 Γ— 10⁹⁷(98-digit number)
12626544056231415903…54023146934338355199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.262 Γ— 10⁹⁷(98-digit number)
12626544056231415903…54023146934338355201
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
2.525 Γ— 10⁹⁷(98-digit number)
25253088112462831806…08046293868676710399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.525 Γ— 10⁹⁷(98-digit number)
25253088112462831806…08046293868676710401
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
5.050 Γ— 10⁹⁷(98-digit number)
50506176224925663612…16092587737353420799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.050 Γ— 10⁹⁷(98-digit number)
50506176224925663612…16092587737353420801
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
1.010 Γ— 10⁹⁸(99-digit number)
10101235244985132722…32185175474706841599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.010 Γ— 10⁹⁸(99-digit number)
10101235244985132722…32185175474706841601
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
2.020 Γ— 10⁹⁸(99-digit number)
20202470489970265444…64370350949413683199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.020 Γ— 10⁹⁸(99-digit number)
20202470489970265444…64370350949413683201
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
Circulating Supply:57,979,614 XPMΒ·at block #6,841,904 Β· updates every 60s
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