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Block #162,517

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/13/2013, 9:03:51 AM Β· Difficulty 9.8612 Β· 6,648,282 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9eeddcbaff863a40820ba0e9a90f4ca4024996042995a975e9b60d8ccea3b94e
View on Chainz β†—

Height

#162,517

Difficulty

9.861204

Transactions

1

Size

198 B

Version

2

Bits

09dc77e4

Nonce

54,989

Timestamp

9/13/2013, 9:03:51 AM

Confirmations

6,648,282

Mined by

⛏️ P2SHAdPf23kymkynHU11focULiT8yrsAX3jtxK

Merkle Root

8cce004838508a9631341b0ce246edc1cc5229e62009a46838a25da21ccbdd85
Transactions (1)
Coinbase8cce004838508a…a25da21ccbdd85
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.

9.215 Γ— 10⁹¹(92-digit number)
92152667859142730920…54033899798270839069
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
9.215 Γ— 10⁹¹(92-digit number)
92152667859142730920…54033899798270839069
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.215 Γ— 10⁹¹(92-digit number)
92152667859142730920…54033899798270839071
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
1.843 Γ— 10⁹²(93-digit number)
18430533571828546184…08067799596541678139
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.843 Γ— 10⁹²(93-digit number)
18430533571828546184…08067799596541678141
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
3.686 Γ— 10⁹²(93-digit number)
36861067143657092368…16135599193083356279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.686 Γ— 10⁹²(93-digit number)
36861067143657092368…16135599193083356281
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
7.372 Γ— 10⁹²(93-digit number)
73722134287314184736…32271198386166712559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.372 Γ— 10⁹²(93-digit number)
73722134287314184736…32271198386166712561
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
1.474 Γ— 10⁹³(94-digit number)
14744426857462836947…64542396772333425119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.474 Γ— 10⁹³(94-digit number)
14744426857462836947…64542396772333425121
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:57,730,491 XPMΒ·at block #6,810,798 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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