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Block #1,611,560

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/2/2016, 10:27:52 PM Β· Difficulty 10.6063 Β· 5,231,391 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9b896d2d5d03f6820aeaf80d987aabbdf868bf1bbb6a9474138f9f481eb72eaf
View on Chainz β†—

Height

#1,611,560

Difficulty

10.606293

Transactions

1

Size

199 B

Version

2

Bits

0a9b35fd

Nonce

428,339,707

Timestamp

6/2/2016, 10:27:52 PM

Confirmations

5,231,391

Mined by

⛏️ P2SHAStjf2S7LLtxdfXgy7wKqLJsVT53GxBz8d

Merkle Root

af499318a576f662ea39a67cdce664be4821f1dffb9ec63a272b1f3a8e126adf
Transactions (1)
Coinbaseaf499318a576f6…2b1f3a8e126adf
1 in β†’ 1 out8.8800 XPM109 B
AStjf2S7…53GxBz8d
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.

9.675 Γ— 10⁹⁴(95-digit number)
96750899689565993913…40859570848243949439
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
9.675 Γ— 10⁹⁴(95-digit number)
96750899689565993913…40859570848243949439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.675 Γ— 10⁹⁴(95-digit number)
96750899689565993913…40859570848243949441
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
1.935 Γ— 10⁹⁡(96-digit number)
19350179937913198782…81719141696487898879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.935 Γ— 10⁹⁡(96-digit number)
19350179937913198782…81719141696487898881
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
3.870 Γ— 10⁹⁡(96-digit number)
38700359875826397565…63438283392975797759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.870 Γ— 10⁹⁡(96-digit number)
38700359875826397565…63438283392975797761
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
7.740 Γ— 10⁹⁡(96-digit number)
77400719751652795130…26876566785951595519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.740 Γ— 10⁹⁡(96-digit number)
77400719751652795130…26876566785951595521
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
1.548 Γ— 10⁹⁢(97-digit number)
15480143950330559026…53753133571903191039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.548 Γ— 10⁹⁢(97-digit number)
15480143950330559026…53753133571903191041
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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