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Block #160,534

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/12/2013, 12:20:31 AM Β· Difficulty 9.8607 Β· 6,635,006 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b9d7e706a50c98b0c72d02c5d36d1bf13de93dea7cff7fbb8de3e5a756216d9b
View on Chainz β†—

Height

#160,534

Difficulty

9.860658

Transactions

2

Size

424 B

Version

2

Bits

09dc5411

Nonce

707,325

Timestamp

9/12/2013, 12:20:31 AM

Confirmations

6,635,006

Mined by

⛏️ P2SHAG7vf4BZznzp2DTDRkEXBgJwey5kU6GCUh

Merkle Root

7ecc10144b6a1b96115195d5dee9fd4a100dcf23b99571572898ba096801462a
Transactions (2)
Coinbasec4295190549432…aa11560408f576
1 in β†’ 1 out10.2800 XPM109 B
AG7vf4BZ…5kU6GCUh
5a74d73d0dee14…df55c5a3c81bc8
1 in β†’ 2 out10.4300 XPM225 B
Acbe8Y18…qNWEBtQuAMdRUVwb…KYR7gmo9
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.

9.058 Γ— 10⁹⁴(95-digit number)
90588190729820687138…99135675591267633039
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
9.058 Γ— 10⁹⁴(95-digit number)
90588190729820687138…99135675591267633039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.058 Γ— 10⁹⁴(95-digit number)
90588190729820687138…99135675591267633041
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
1.811 Γ— 10⁹⁡(96-digit number)
18117638145964137427…98271351182535266079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.811 Γ— 10⁹⁡(96-digit number)
18117638145964137427…98271351182535266081
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
3.623 Γ— 10⁹⁡(96-digit number)
36235276291928274855…96542702365070532159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.623 Γ— 10⁹⁡(96-digit number)
36235276291928274855…96542702365070532161
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
7.247 Γ— 10⁹⁡(96-digit number)
72470552583856549711…93085404730141064319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.247 Γ— 10⁹⁡(96-digit number)
72470552583856549711…93085404730141064321
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
1.449 Γ— 10⁹⁢(97-digit number)
14494110516771309942…86170809460282128639
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9

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:57,608,385 XPMΒ·at block #6,795,539 Β· updates every 60s
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