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Block #204,600

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/11/2013, 2:47:48 PM Β· Difficulty 9.8987 Β· 6,603,286 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
023e8c05c3bb441a04b42b31dfed0431c2f60d390bb4266777aa89adf6ce0db1
View on Chainz β†—

Height

#204,600

Difficulty

9.898724

Transactions

1

Size

198 B

Version

2

Bits

09e612cf

Nonce

26,200

Timestamp

10/11/2013, 2:47:48 PM

Confirmations

6,603,286

Mined by

⛏️ P2SHASHCgr3FcMvAMVeUbxmte178wGe7VPFbY8

Merkle Root

5264e29964698e0c19dd7955a3dcf594d5aa66a0e43877ab12d8b318ce28ba49
Transactions (1)
Coinbase5264e29964698e…d8b318ce28ba49
1 in β†’ 1 out10.1900 XPM109 B
ASHCgr3F…e7VPFbY8
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.

1.481 Γ— 10⁹²(93-digit number)
14818906895182784616…72792598333840972799
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
1.481 Γ— 10⁹²(93-digit number)
14818906895182784616…72792598333840972799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.481 Γ— 10⁹²(93-digit number)
14818906895182784616…72792598333840972801
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
2.963 Γ— 10⁹²(93-digit number)
29637813790365569232…45585196667681945599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.963 Γ— 10⁹²(93-digit number)
29637813790365569232…45585196667681945601
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
5.927 Γ— 10⁹²(93-digit number)
59275627580731138465…91170393335363891199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.927 Γ— 10⁹²(93-digit number)
59275627580731138465…91170393335363891201
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
1.185 Γ— 10⁹³(94-digit number)
11855125516146227693…82340786670727782399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.185 Γ— 10⁹³(94-digit number)
11855125516146227693…82340786670727782401
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
2.371 Γ— 10⁹³(94-digit number)
23710251032292455386…64681573341455564799
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:57,707,123 XPMΒ·at block #6,807,885 Β· updates every 60s
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