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Block #162,535

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/13/2013, 9:16:15 AM Β· Difficulty 9.8614 Β· 6,640,022 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
de3f1a78a2566cbb29e7b6b6b515c6ada3e5a8bfdbf0ad3f2bf9e333fbe78a95
View on Chainz β†—

Height

#162,535

Difficulty

9.861428

Transactions

3

Size

1.27 KB

Version

2

Bits

09dc8684

Nonce

125,974

Timestamp

9/13/2013, 9:16:15 AM

Confirmations

6,640,022

Mined by

⛏️ P2SHAJHy63jeXcWP53SoT3cmtwSrEvgcpU5UnY

Merkle Root

7ed07613014f5094747184362bfe1dbf21112f07d6e5ef9dde083e3168395299
Transactions (3)
Coinbasea0b4adf5778ba4…935a6776cb88be
1 in β†’ 1 out10.2900 XPM109 B
AJHy63je…gcpU5UnY
4143d1e575c872…f06b15d5d84903
4 in β†’ 1 out41.0700 XPM499 B
AU63Ubwp…RaoT2ZVk
bd0475f7ab96b3…ee4f2523c43821
4 in β†’ 1 out11.0000 XPM601 B
AFz9fXym…wh4UqpkL
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.

1.003 Γ— 10⁹⁡(96-digit number)
10033184967627878061…84771705017090041159
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
1.003 Γ— 10⁹⁡(96-digit number)
10033184967627878061…84771705017090041159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.003 Γ— 10⁹⁡(96-digit number)
10033184967627878061…84771705017090041161
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
2.006 Γ— 10⁹⁡(96-digit number)
20066369935255756122…69543410034180082319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.006 Γ— 10⁹⁡(96-digit number)
20066369935255756122…69543410034180082321
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
4.013 Γ— 10⁹⁡(96-digit number)
40132739870511512244…39086820068360164639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.013 Γ— 10⁹⁡(96-digit number)
40132739870511512244…39086820068360164641
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
8.026 Γ— 10⁹⁡(96-digit number)
80265479741023024489…78173640136720329279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.026 Γ— 10⁹⁡(96-digit number)
80265479741023024489…78173640136720329281
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
1.605 Γ— 10⁹⁢(97-digit number)
16053095948204604897…56347280273440658559
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:57,664,469 XPMΒ·at block #6,802,556 Β· updates every 60s
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