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Block #1,104,085

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/14/2015, 8:07:33 AM Β· Difficulty 10.7654 Β· 5,711,853 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
58464f584a841b545a8d91ea8d28abf1cbd90413320be72a3ef67db64dc67feb
View on Chainz β†—

Height

#1,104,085

Difficulty

10.765385

Transactions

3

Size

1.47 KB

Version

2

Bits

0ac3f040

Nonce

1,648,323,126

Timestamp

6/14/2015, 8:07:33 AM

Confirmations

5,711,853

Mined by

⛏️ P2SHAdHkrjE74Y3LtEgkKomxx2w1trAnWsZFGc

Merkle Root

6f4c382ce8036435b91dd7eb41e62f34868f674f8756272c8bee6bfad40b4970
Transactions (3)
Coinbasecb8e8459a00c73…a73b305be3b440
1 in β†’ 1 out8.6400 XPM109 B
AdHkrjE7…AnWsZFGc
abe8bc6b1c4ca7…31e0b030dfb3cd
6 in β†’ 2 out28.9323 XPM967 B
AJdM6BQD…g1g59wtyAchar9Tv…vCv8ygEb
1d25d431f791f1…a0b268dfd12395
2 in β†’ 1 out10.1349 XPM340 B
APT3Ge1c…FTCL7e3u
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.

2.097 Γ— 10⁹⁴(95-digit number)
20973317222944130444…39302997056200668199
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
2.097 Γ— 10⁹⁴(95-digit number)
20973317222944130444…39302997056200668199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.097 Γ— 10⁹⁴(95-digit number)
20973317222944130444…39302997056200668201
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
4.194 Γ— 10⁹⁴(95-digit number)
41946634445888260889…78605994112401336399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.194 Γ— 10⁹⁴(95-digit number)
41946634445888260889…78605994112401336401
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
8.389 Γ— 10⁹⁴(95-digit number)
83893268891776521778…57211988224802672799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.389 Γ— 10⁹⁴(95-digit number)
83893268891776521778…57211988224802672801
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
1.677 Γ— 10⁹⁡(96-digit number)
16778653778355304355…14423976449605345599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.677 Γ— 10⁹⁡(96-digit number)
16778653778355304355…14423976449605345601
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
3.355 Γ— 10⁹⁡(96-digit number)
33557307556710608711…28847952899210691199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.355 Γ— 10⁹⁡(96-digit number)
33557307556710608711…28847952899210691201
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:57,771,617 XPMΒ·at block #6,815,937 Β· updates every 60s
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