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Block #2,184,365

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/29/2017, 8:11:43 AM Β· Difficulty 10.9429 Β· 4,648,430 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
034604fd0532162e973dc00b3184da9a23c76a846e81ffff794379ec2265e8df
View on Chainz β†—

Height

#2,184,365

Difficulty

10.942902

Transactions

1

Size

201 B

Version

2

Bits

0af16205

Nonce

11,068,423

Timestamp

6/29/2017, 8:11:43 AM

Confirmations

4,648,430

Mined by

⛏️ P2SHAGGpfgzn646xH3Q5sSdQgEV4LvhVg8KES5

Merkle Root

b8d1c0a700a5bed33ed6a9ecbe5c51be040dcc96b36f3845399ebfbda70d6c62
Transactions (1)
Coinbaseb8d1c0a700a5be…9ebfbda70d6c62
1 in β†’ 1 out8.3400 XPM110 B
AGGpfgzn…hVg8KES5
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.

1.494 Γ— 10⁹⁢(97-digit number)
14940163409580051985…36478712741409007359
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
1.494 Γ— 10⁹⁢(97-digit number)
14940163409580051985…36478712741409007359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.494 Γ— 10⁹⁢(97-digit number)
14940163409580051985…36478712741409007361
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
2.988 Γ— 10⁹⁢(97-digit number)
29880326819160103971…72957425482818014719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.988 Γ— 10⁹⁢(97-digit number)
29880326819160103971…72957425482818014721
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
5.976 Γ— 10⁹⁢(97-digit number)
59760653638320207943…45914850965636029439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.976 Γ— 10⁹⁢(97-digit number)
59760653638320207943…45914850965636029441
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
1.195 Γ— 10⁹⁷(98-digit number)
11952130727664041588…91829701931272058879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.195 Γ— 10⁹⁷(98-digit number)
11952130727664041588…91829701931272058881
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
2.390 Γ— 10⁹⁷(98-digit number)
23904261455328083177…83659403862544117759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.390 Γ— 10⁹⁷(98-digit number)
23904261455328083177…83659403862544117761
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:57,906,528 XPMΒ·at block #6,832,794 Β· updates every 60s
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