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Block #161,506

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/12/2013, 5:12:44 PM Β· Difficulty 9.8595 Β· 6,648,949 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cc6c1f2f1da0a582bf9eb31b3f907261a8b9d3517058c6df4fb20ec8fb9a80dc
View on Chainz β†—

Height

#161,506

Difficulty

9.859506

Transactions

1

Size

199 B

Version

2

Bits

09dc0890

Nonce

23,839

Timestamp

9/12/2013, 5:12:44 PM

Confirmations

6,648,949

Mined by

⛏️ P2SHAdPf23kymkynHU11focULiT8yrsAX3jtxK

Merkle Root

e1039fbb0bee6610093326a0aa21f632219bc71df85b94768f0fdbd51da0bce6
Transactions (1)
Coinbasee1039fbb0bee66…0fdbd51da0bce6
1 in β†’ 1 out10.2700 XPM109 B
AdPf23ky…sAX3jtxK
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.

1.224 Γ— 10⁹⁡(96-digit number)
12249601962710340894…45456291722034291199
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
1.224 Γ— 10⁹⁡(96-digit number)
12249601962710340894…45456291722034291199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.224 Γ— 10⁹⁡(96-digit number)
12249601962710340894…45456291722034291201
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
2.449 Γ— 10⁹⁡(96-digit number)
24499203925420681789…90912583444068582399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.449 Γ— 10⁹⁡(96-digit number)
24499203925420681789…90912583444068582401
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
4.899 Γ— 10⁹⁡(96-digit number)
48998407850841363578…81825166888137164799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.899 Γ— 10⁹⁡(96-digit number)
48998407850841363578…81825166888137164801
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
9.799 Γ— 10⁹⁡(96-digit number)
97996815701682727157…63650333776274329599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.799 Γ— 10⁹⁡(96-digit number)
97996815701682727157…63650333776274329601
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
1.959 Γ— 10⁹⁢(97-digit number)
19599363140336545431…27300667552548659199
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:57,727,726 XPMΒ·at block #6,810,454 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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