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Block #133,673

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/25/2013, 4:02:50 PM Β· Difficulty 9.7959 Β· 6,662,163 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d2bfd4d76dc6df4da067928518a123df81c322c06f09da8f503b2e059156ec26
View on Chainz β†—

Height

#133,673

Difficulty

9.795916

Transactions

2

Size

721 B

Version

2

Bits

09cbc122

Nonce

5,012

Timestamp

8/25/2013, 4:02:50 PM

Confirmations

6,662,163

Mined by

⛏️ P2SHASrk1Kp96c577UeqczcmgNxAWV2HXGP3jF

Merkle Root

5f4273dbdb21fa9e258a75d9103ef80dc1a37e9c165c7c22beb2685e4f8e797d
Transactions (2)
Coinbase5e76d555ee49c4…c30e1852e9ea6f
1 in β†’ 1 out10.4200 XPM109 B
ASrk1Kp9…2HXGP3jF
3887cd53440c3e…8864e862b266c8
3 in β†’ 2 out200.0107 XPM522 B
Ab7iXvjf…LnFwMDZnAX12WUWr…F9w19Wqj
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.

2.899 Γ— 10⁹³(94-digit number)
28995410797508320541…96045469278199500799
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
2.899 Γ— 10⁹³(94-digit number)
28995410797508320541…96045469278199500799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.899 Γ— 10⁹³(94-digit number)
28995410797508320541…96045469278199500801
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
5.799 Γ— 10⁹³(94-digit number)
57990821595016641083…92090938556399001599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.799 Γ— 10⁹³(94-digit number)
57990821595016641083…92090938556399001601
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
1.159 Γ— 10⁹⁴(95-digit number)
11598164319003328216…84181877112798003199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.159 Γ— 10⁹⁴(95-digit number)
11598164319003328216…84181877112798003201
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
2.319 Γ— 10⁹⁴(95-digit number)
23196328638006656433…68363754225596006399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.319 Γ— 10⁹⁴(95-digit number)
23196328638006656433…68363754225596006401
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
4.639 Γ— 10⁹⁴(95-digit number)
46392657276013312867…36727508451192012799
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:57,610,771 XPMΒ·at block #6,795,835 Β· updates every 60s
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