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Block #219,869

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/20/2013, 5:39:38 PM Β· Difficulty 9.9344 Β· 6,596,726 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
558f50dc300aa5c809b7c6a7d6ece93d438c87593e2c9b2fef4ad793d41dedc9
View on Chainz β†—

Height

#219,869

Difficulty

9.934428

Transactions

1

Size

200 B

Version

2

Bits

09ef36ab

Nonce

31,738

Timestamp

10/20/2013, 5:39:38 PM

Confirmations

6,596,726

Mined by

⛏️ P2SHAMjEL5jU5FrR33MFDHGMbVsnwkXWAbZRhp

Merkle Root

36cfaa47a86b4fa7315d26cb9e1df7723a888fbb02f1bd4288277e493b97a82c
Transactions (1)
Coinbase36cfaa47a86b4f…277e493b97a82c
1 in β†’ 1 out10.1200 XPM109 B
AMjEL5jU…XWAbZRhp
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.

5.929 Γ— 10⁹⁢(97-digit number)
59291788084343150282…99921410304128006719
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
5.929 Γ— 10⁹⁢(97-digit number)
59291788084343150282…99921410304128006719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.929 Γ— 10⁹⁢(97-digit number)
59291788084343150282…99921410304128006721
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
1.185 Γ— 10⁹⁷(98-digit number)
11858357616868630056…99842820608256013439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.185 Γ— 10⁹⁷(98-digit number)
11858357616868630056…99842820608256013441
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
2.371 Γ— 10⁹⁷(98-digit number)
23716715233737260112…99685641216512026879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.371 Γ— 10⁹⁷(98-digit number)
23716715233737260112…99685641216512026881
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
4.743 Γ— 10⁹⁷(98-digit number)
47433430467474520225…99371282433024053759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.743 Γ— 10⁹⁷(98-digit number)
47433430467474520225…99371282433024053761
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
9.486 Γ— 10⁹⁷(98-digit number)
94866860934949040451…98742564866048107519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.486 Γ— 10⁹⁷(98-digit number)
94866860934949040451…98742564866048107521
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:57,776,885 XPMΒ·at block #6,816,594 Β· updates every 60s
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