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Block #2,682,897

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/29/2018, 10:46:36 AM Β· Difficulty 11.6909 Β· 4,158,767 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6fdee2c13085eb5307e3d11d05d00da1a6a3fb3b5283e7fbd15ba3488d32cefe
View on Chainz β†—

Height

#2,682,897

Difficulty

11.690923

Transactions

2

Size

573 B

Version

2

Bits

0bb0e055

Nonce

278,356,931

Timestamp

5/29/2018, 10:46:36 AM

Confirmations

4,158,767

Mined by

⛏️ P2SHAGH4USMja4U8yCqDQED2FAEbhNmghnca5z

Merkle Root

97b803cc7db3920c838bab9925eb513fbc45c2cbfbd9c04e61f368774e803a9d
Transactions (2)
Coinbaseef83ce6751ef21…3eba387fc912fd
1 in β†’ 1 out7.3100 XPM109 B
AGH4USMj…mghnca5z
4a84c39bef6ba8…60f8108b60accf
2 in β†’ 2 out14.6230 XPM374 B
AZheuN7g…nUhQyHgeAdUbFbQ9…MXLm2P1G
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.

3.547 Γ— 10⁹⁴(95-digit number)
35471104299393353346…52080966142098745399
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
3.547 Γ— 10⁹⁴(95-digit number)
35471104299393353346…52080966142098745399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.547 Γ— 10⁹⁴(95-digit number)
35471104299393353346…52080966142098745401
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
7.094 Γ— 10⁹⁴(95-digit number)
70942208598786706692…04161932284197490799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.094 Γ— 10⁹⁴(95-digit number)
70942208598786706692…04161932284197490801
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
1.418 Γ— 10⁹⁡(96-digit number)
14188441719757341338…08323864568394981599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.418 Γ— 10⁹⁡(96-digit number)
14188441719757341338…08323864568394981601
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
2.837 Γ— 10⁹⁡(96-digit number)
28376883439514682676…16647729136789963199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.837 Γ— 10⁹⁡(96-digit number)
28376883439514682676…16647729136789963201
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
5.675 Γ— 10⁹⁡(96-digit number)
56753766879029365353…33295458273579926399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.675 Γ— 10⁹⁡(96-digit number)
56753766879029365353…33295458273579926401
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
1.135 Γ— 10⁹⁢(97-digit number)
11350753375805873070…66590916547159852799
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:57,977,701 XPMΒ·at block #6,841,663 Β· updates every 60s
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