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Block #2,849,507

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/21/2018, 5:19:00 PM Β· Difficulty 11.7312 Β· 3,987,726 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1d4568a5879bdc47910f69269c74dceeda5dc89e65d0e5305b5ac2f19d5e1fec
View on Chainz β†—

Height

#2,849,507

Difficulty

11.731217

Transactions

1

Size

200 B

Version

2

Bits

0bbb310d

Nonce

1,950,917,236

Timestamp

9/21/2018, 5:19:00 PM

Confirmations

3,987,726

Mined by

⛏️ P2SHAeRVJzRCkMnqswUPvwAXvRyaPYCnqiy1WW

Merkle Root

15cb713b0f0bb57a8ddf5816c00058323d0b82f40e4fb5c867c35f3747c3d74d
Transactions (1)
Coinbase15cb713b0f0bb5…c35f3747c3d74d
1 in β†’ 1 out7.2500 XPM109 B
AeRVJzRC…Cnqiy1WW
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.

2.830 Γ— 10⁹⁢(97-digit number)
28308602782436732203…43940277024926689279
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
2.830 Γ— 10⁹⁢(97-digit number)
28308602782436732203…43940277024926689279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.830 Γ— 10⁹⁢(97-digit number)
28308602782436732203…43940277024926689281
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
5.661 Γ— 10⁹⁢(97-digit number)
56617205564873464406…87880554049853378559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.661 Γ— 10⁹⁢(97-digit number)
56617205564873464406…87880554049853378561
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
1.132 Γ— 10⁹⁷(98-digit number)
11323441112974692881…75761108099706757119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.132 Γ— 10⁹⁷(98-digit number)
11323441112974692881…75761108099706757121
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
2.264 Γ— 10⁹⁷(98-digit number)
22646882225949385762…51522216199413514239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.264 Γ— 10⁹⁷(98-digit number)
22646882225949385762…51522216199413514241
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
4.529 Γ— 10⁹⁷(98-digit number)
45293764451898771525…03044432398827028479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.529 Γ— 10⁹⁷(98-digit number)
45293764451898771525…03044432398827028481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
9.058 Γ— 10⁹⁷(98-digit number)
90587528903797543050…06088864797654056959
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,942,180 XPMΒ·at block #6,837,232 Β· updates every 60s
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