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Block #183,020

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/27/2013, 5:39:50 PM Β· Difficulty 9.8577 Β· 6,622,791 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cffc6e6f92b5cec582682177876389dee05c05cd77c9dd43267c68f8569b5cf0
View on Chainz β†—

Height

#183,020

Difficulty

9.857736

Transactions

1

Size

200 B

Version

2

Bits

09db949c

Nonce

70,669

Timestamp

9/27/2013, 5:39:50 PM

Confirmations

6,622,791

Mined by

⛏️ P2SHAHnBbSZUB33VknNc1hSqs87dGJRVfat6WW

Merkle Root

0f5c890c03c3ab2f27e118597c38e5f8d7d0cb50b0e4ec7836d3b7efb2ac843c
Transactions (1)
Coinbase0f5c890c03c3ab…d3b7efb2ac843c
1 in β†’ 1 out10.2800 XPM109 B
AHnBbSZU…RVfat6WW
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.

1.887 Γ— 10⁹⁷(98-digit number)
18871015023054967639…34386341275827127199
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
1.887 Γ— 10⁹⁷(98-digit number)
18871015023054967639…34386341275827127199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.887 Γ— 10⁹⁷(98-digit number)
18871015023054967639…34386341275827127201
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
3.774 Γ— 10⁹⁷(98-digit number)
37742030046109935278…68772682551654254399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.774 Γ— 10⁹⁷(98-digit number)
37742030046109935278…68772682551654254401
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
7.548 Γ— 10⁹⁷(98-digit number)
75484060092219870557…37545365103308508799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.548 Γ— 10⁹⁷(98-digit number)
75484060092219870557…37545365103308508801
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
1.509 Γ— 10⁹⁸(99-digit number)
15096812018443974111…75090730206617017599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.509 Γ— 10⁹⁸(99-digit number)
15096812018443974111…75090730206617017601
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
3.019 Γ— 10⁹⁸(99-digit number)
30193624036887948222…50181460413234035199
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:57,690,574 XPMΒ·at block #6,805,810 Β· updates every 60s
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