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Block #1,611,417

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/2/2016, 7:58:32 PM Β· Difficulty 10.6069 Β· 5,231,540 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
29aa8407fe079e74710e4640625fed2ffcb38202d925d3ff0acbd70283bdbca0
View on Chainz β†—

Height

#1,611,417

Difficulty

10.606945

Transactions

1

Size

198 B

Version

2

Bits

0a9b60bd

Nonce

425,735,463

Timestamp

6/2/2016, 7:58:32 PM

Confirmations

5,231,540

Mined by

⛏️ P2SHAZCwzCn2LdT13NziUt6ZUpZWHCwxSoKZ2D

Merkle Root

c8603b3fec155606d88479ab969d83a38c216c68d8d21028cc8e219be001a7ce
Transactions (1)
Coinbasec8603b3fec1556…8e219be001a7ce
1 in β†’ 1 out8.8700 XPM109 B
AZCwzCn2…wxSoKZ2D
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.

1.597 Γ— 10⁹²(93-digit number)
15970138010653559701…03404568572009290879
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
1.597 Γ— 10⁹²(93-digit number)
15970138010653559701…03404568572009290879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.597 Γ— 10⁹²(93-digit number)
15970138010653559701…03404568572009290881
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
3.194 Γ— 10⁹²(93-digit number)
31940276021307119402…06809137144018581759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.194 Γ— 10⁹²(93-digit number)
31940276021307119402…06809137144018581761
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
6.388 Γ— 10⁹²(93-digit number)
63880552042614238804…13618274288037163519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.388 Γ— 10⁹²(93-digit number)
63880552042614238804…13618274288037163521
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
1.277 Γ— 10⁹³(94-digit number)
12776110408522847760…27236548576074327039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.277 Γ— 10⁹³(94-digit number)
12776110408522847760…27236548576074327041
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
2.555 Γ— 10⁹³(94-digit number)
25552220817045695521…54473097152148654079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.555 Γ— 10⁹³(94-digit number)
25552220817045695521…54473097152148654081
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:57,988,009 XPMΒ·at block #6,842,956 Β· updates every 60s
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